European Journal of Orthodontics 20 (1998) 347-356 1998 European Orthodontic Society

Biomechanical effects of rapid maxillary expansionon the craniofacial skeleton, studied by the finiteelement methodHaluk lseri", A. Erman Tekkaya**, Orner Oztan** and Sadik Bilgi~****Department of Orthodontics, School of Dentistry, University of Ankara,**Department of Mechanical Engineering, Middle East Technical University, Ankara and***Department of Radiology, Faculty of Medicine, University of Ankara, Turkey

SUMMARY The aim of this study was to evaluate the biomechanical effect of rapid maxillaryexpansion (RME) on the craniofacial complex by using a three-dimensional finite elementmodel (FEM) of the craniofacial skeleton. The construction of the three-dimensional FEMwas based on computer tomography (CT) scans of the skull of a 12-year-old male subject.The CT pictures were digitized and converted to the finite element model by means of aprocedure developed for the present study. The final mesh consisted of 2270 thick shellelements with 2120 nodes. The mechanical response in terms of displacement and vonMises stresses was determined by expanding the maxilla up to 5 mm on both sides. Viewedocclusally, the two halves of the maxilla were separated almost in a parallel manner during1-, 3-, and 5-mm expansions. The greatest widening was observed in the dento-alveolarareas, and gradually decreased through the superior structures. The width of the nasal cavityat the floor of the nose increased markedly. However, the postero-superior part of the nasalcavity was moved slightly medially. No displacement was observed in the parietal, frontaland occipital bones. High stress levels were observed in the canine and molar regions ofthe maxilla, lateral wall of the inferior nasal cavity, zygomatic and nasal bones, with thehighest stress concentration at the pterygoid plates of the sphenoid bone in the regionclose to the cranial base.

Introduction

Rapid maxillary expansion (RME) procedureshave been used over the past century (Angell,1860), and have been shown to be a valuable aidin the orthodontic treatment of young patientsexhibiting maxillary collapse, pseudo-Class IIImalocclusions, and rhinological and respiratoryailments (Haas, 1970, 1980; Wertz, 1970; Graberand Swain, 1975; Bishara and Staley, 1987).

Different types of RME devices have beenused by clinicians and many studies have beenconducted to investigate the response of thecraniofacial complex. Isaacson et al. (1964), andIsaacson and Ingram (1964) measured forcescreated by a rapid palatal expansion appliance,and reported that a single activation created

between 3 and 10 pounds of force that decayedrapidly at first and continued to decrease slowly.In 1965, Zimring and Isaacson found that maxi-mum forces during RME treatment ranged from16.6 to 34.8 lb. Gardner and Kronman (1971)showed evidence of distortions in the lambdoidand parietal sutures in rhesus monkeys, as wellas in the spheno-occipital synchondrosis. Storey(1973) illustrated that palatal expansion wasgreater at the alveolar crest and less at thepalatal vault, and that the maxillary bones swinglaterally with the centre of rotation near thenasofrontal suture. In a study on a human dryskull, Kudlick (1973) concluded that all cranio-facial bones directly articulating with the maxillawere displaced, except the sphenoid bone. Wertzand Dreskin (1977) showed that the maxilla

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moved downward and usually forward duringsuture opening, while Timms (1980) showed thatthe maxilla and palatine bones moved apart,along with the pterygoid processes of the sphen-oid bone. Chaconas and Caputo (1982) duplicateda three-dimensional photo-elastic model froma human skull, and reported that the activatedRME appliances produced stresses that radiatedsuperiorly along the perpendicular plates of thepalatine bone to deeper anatomical structures,such as the lacrimal and nasal bones, as well asthe pterygoid plates of the sphenoid.

Although previous studies have provideddetailed knowledge regarding the RME tech-nique, the effects of the procedure still remainunclear due to the limited evaluation of the bio-mechanical effects on the internal structuresof the craniofacial complex. The finite elementmethod, which has been applied in the mech-anical analysis of stresses and strains in the fieldof engineering, makes it practicable to elucidatethe biomechanical state variables such as displace-ments, strains and stresses induced in livingstructures by various external forces (Tanneet al., 1989a,b). Therefore, the aim of this studywas to evaluate the biomechanical effects ofRME on the craniofacial complex by using theFEM as applied to the three-dimensional modelof a human skull.

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H. ISERI ET AL.

a

bMaterials and methods

The finite element analysis was performed on amodel of the cranium of a 12-year-old male, witha narrow maxillary base and bilateral posteriorcrossbite. The subject showed no craniofacialanomaly, and RME treatment was indicatedaccording to the skeletal and dento-alveolaranalyses. The geometry of the cranium wasobtained by using the computer tomography (CT)technique (Figure 1). The cranium was orientatedso that the plane of section passed perpendicularto the orbito-mental plane. CT-images weretaken at 5-mm intervals in the parallel horizontalplanes. This spacing of CT-images enables ahigher geometric accuracy than that used byTanne et al. (1987; 10 mm) and von Ehler et al.(1975; 30 mm). To verify the model slices in thevertical plane, the geometry-generation phase

cFigure 1 Basic steps of generating the finite elementmodel of the cranium: (a) Sample slices obtained by com-puter tomography. (b) Geometric lines generated by usinggeometric points assigned along the midline of the skullbone. (c) Geometric surfaces generated from geometriclines.

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was also considered. Hart et al. (1992) reportedthat the positioning error during the scanning ofCT-images was approximately 1 mm. This corres-ponds to an average position error of 0.5 per centfor the present cranium, which is acceptable.The images were scanned and digitized yieldingthe centrelines between the inner and outer boneboundary as well as the respective bone thicknessat typical locations. Along the bone-centreline ofeach CT-image, geometric points were definedsuch that geometric lines passing through thesepoints describe the measured bone geometry asclose as possible. The straight lines approximateda curved skull section in such a way that approx-imately 10 straight line segments were used forthe representation of a semi-circle. This intro-duced an error of approximately 0.4 per centin the arch length of the cranium-model. Thegeometric points between two neighbouringCT-images were also connected by straight linesforming flat triangular or quadrilateral surfacesbetween the horizontal slices (Figure 1). Theerror resulting due to these flat surface betweenCT-image-planes was in the same range as thatfor the straight line approximation. Finally, thesesurfaces were used to generate the finite elementmesh as shown in Figure 2. Due to symmetry,only one half of the cranium with respect to thesagittal plane passing between the orbita wasconsidered. The mandible was not modelled.Therefore, it can be concluded that the accuracyof the geometric model of the present study,obtained from CT-images is satisfactory from anengineering point of view.

The finite element computations were con-ducted using linear shell elements which wereable to take into account membrane, i.e. in-plane,deformations as well as bending deformations.Due to these effects, it is necessary to constructthe finite element model so that these effects canbe considered. The use of standard solid (brick)elements as studied by Tanne et al. (1987) cannotdescribe bending effects, especially if only oneelement is used across the bone thickness (seeOztan, 1995). In this study, the QUAD4 (warpedquadrilateral shell element) and the TRUMP (atriangular plane membrane-bending element)elements of the ASKA element library havebeen used. Both elements have 6 degrees of

349

Figure 2 Three-dimensional finite element model of thecraniofacial complex. The model consists of 2349 quad-rilateral and triangular thick shell elements with 2147nodes. At each node three translational and three rotationaldegress of freedom are defined.

freedom (three transitional and three rotational)per node. The thickness of the shell can varyfrom node to node for both element types. Themesh density of the model was determined bymeans of a standard convergence study: threemeshes were constructed with 1590 (coarse), 5892(medium), and 12882 (fine) degrees of freedom,respectively. For a critical point, for instance theroot of the canine, total displacement valuesshowed a difference of 25 per cent for the coarsemesh as compared with the medium mesh andonly 4.7 per cent difference for the medium meshas compared with the fine mesh. These resultsindicate that the error due to the topology of themesh can be estimated as 1 to 2 per cent, since allcomputations of the RME-study were conductedwith the fine mesh.

Solid parts in the interior of the cranium, aswell as the maxilla including the teeth, were alsomodelled with shell elements, which is obviouslya crude idealization. For these areas, the thick-ness of the shell elements was increased, accord-ing to the geometric dimensions of the respectivepart so that an equivalent stiffness effect wassimulated.

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350 H. ISERI ET AL.

Table 1 Displacementsand stress distributions with5 mm of RME (x, y and z represent displacementsin thetransversal, sagittal and vertical planes, respectively).

Structure under analysis

Incisal tip of the maxillary central incisorCusp of the first molarMaxillary bone at the incisor regionMaxillary bone at the canine regionMaxillary bone at the molar regionAnterior part of the palatePalatinal boneInferior part of the pterygoid plateMiddle part of the pterygoid plateSuperior part of the pterygoid plateAnterior-superior part of the zygomatic boneAnterior part of the arcus zygomaticusPosterior part of the arcus zygomaticusAnterior-inferior part of the outer nasal wallPosterior-inferior part of the outer nasal wallPosterior-superior part of the outer nasal wallExternal wall of the orbitaNasal boneFrontal boneParietal boneParse squamosa of the temporal boneSquamo of the occipital bone

The materials in the analysis were assumed tobe linearly elastic and isotropic. Three differenttypes of material were considered: compact bone,cancellous bone, and tooth. The elastic proper-ties for these materials are taken from Tanneet al. (1987). All sutures were assumed to havethe same mechanical properties as the surround-ing bone material except at the palatinal bone.The two parts of the palatinal bone which areseparated by the vertical plane of symmetrywere assumed to be unconnected, so that theymove freely in lateral directions with respect tothe vertical plane of symmetry.

All points of the cranium lying on the sym-metry plane are constrained to have no motionperpendicular to this plane. An exception forthis boundary condition were the points at thepalatinal bone which were left completelyunconstrained. Furthermore, to ensure a uniquesolution, rigid-body motions were prevented byconstraining all degrees of freedom of the nodesalong the foramen magnum.

Displacement (mm) Max.v. Mises stress(kg/rum')

x y z

5 1.4 1.4 0.725 1.4 0.8 2.094.99 2.1 1.2 2.294.99 2.1 1.1 18.824.91 2.0 0.4 15.724.9 2.1 1.1 2.094.8 2.1 0.2 0.964.9 1.8 0.04 6.204.8 2.1 0.01 26.951.4 1.6 0.7 73.753.9 1.6 0.4 41.253.3 0.7 -0.4 4.280.6 -0.04 -0.2 0.444.8 2.1 1.1 30.794.8 2.1 0.02 4.95

-0.3 0.2 1.1 12.281.6 0.04 -0.3 14.060.3 -1.2 1.1 16.290.03 -0.2 0.5 2.650.0001 -0.05 0.02 0.070.1 0.08 -0.4 11.59

-0.002 -0.02 0.02 0.50

In this study, it was assumed that the twoplates of the RME device moved apart by adistance of 2,6, and 10 mm. Therefore, boundaryconditions on the maxillary canine, premolars,and first molar teeth were assigned as theprescribed transversal displacement with magni-tudes of 1, 3, and 5 mm, respectively. The RMEplates were assumed to be rigid.

Results

Table 1 shows the three-dimensional pattern ofdisplacements and stress distributions observedat 22 anatomical structures located in the cranio-facial complex. The findings show that thedisplacements at the nodes varied linearly forthe given displacement boundary conditions dueto the RME. This is an expected result since theproblem is linear and hence the results varylinearly with the loading. Viewed occlusally,the two halves of the maxillary dento-alveolarcomplex, basal maxilla, and lateral walls of the

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BIOMECHANICAL EFFECTS OF RME 351

~xz

Figure 3 Pattern of computed displacements (- - - - -unloaded; -- loaded) of the nasomaxillary complex,with 5 mm of RME. Note that the centre of rotation islocated at the frontal bone.

nasal cavity separated almost in a parallel manner.On the other hand, the antero-superior part ofthe upper nasal cavity separated more than thepostero-superior part. No lateral displacementwas observed at the temporal, parietal, frontal,sphenoid, and occipital bones. The greatest widen-ing was observed in the dento-alveolar areas,gradually decreasing through the upper struc-tures (Figure 3). The width of the nasal cavity atthe floor of the nose increased markedly, whilethe postero-superior part of the nasal cavity wasmoved slightly medially. Maxillary bone, maxil-lary central incisors, and molars were slightlydisplaced downwards and forwards. The anteriorregion of the palate and nasal floor descendedmore than the posterior region. Similarly, themaxillary central incisors displaced downwardsmore than the maxillary first molars (Figure 4).

The magnitude and distribution of maximumvon Mises stresses produced at various areasof the craniofacial complex by the activation ofRME device, up to 5 mm on each side, are shownin Table 1 and Figure 5. Highest stress levels were

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Figure4 (a) Total, (b) transversal, (c) sagittal, and (d) vertical computed displacement field of the skeletal structures in thecraniofacial complex with 5 mm of RME. Red coloured areas represent the structures displaced at least 3 mm.

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Kglmm2

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i 0Figure 5 Stress distribution (von Mises; kg/mm-) in thecraniofacial complex with 5 mm of RME. Only the maxi-mum values across the thickness are considered. Redcoloured areas represent the structures under stress ofmore than 20 kg/mrn",

observed in the pterygoid plate of the sphenoidbone and zygomatic bone. The findings indicatedthat high stresses produced by the RME are espe-cially located in the superior parts of the pterygoidprocesses of the sphenoid bone (73.75 kg/rnm-).High stress levels were found at the externalsurface of the zygomatic bone and external wallof the orbita, and decreased along the arcuszygomaticus. In the maxilla, high stresses wereobserved at the canine and molar regions (18.82and 15.72 kg/rnm/, respectively), and were alsofound around the nasal bone and nasal cavity,especially in the antero-inferior wall of the nasalcavity (30.79 kg/mm-), In the frontal, parietal,temporal and occipital bones, RME producedstress levels ranging from 0.07 to 11.59 kg/mm/.

Discussion

Several studies have been conducted to investi-gate histologically, morphologically and biomech-anically the response of the craniofacial complexto RME. During orthodontic treatment, thecraniofacial skeleton is subjected to complexloading and it would be difficult to assess themechanical reaction of the craniofacial bones tocomplex loading in three-dimensional spaceby using conventional methods, namely, straingauge (Tanne et al., 1985), photoelastic (Chaconas

H. ISERI ET AL.

and Caputo, 1982) or holographic (Pavlin andVukicevic, 1984) techniques. In addition, it hasbeen suggested that by using roentgenographiccephalometric methods (RCM) only anecdotalobservations are possible and RCMs are incap-able of correctly depicting, in detail, time-relatedchanges or changes in location of biologicalshapes (Moyers and Bookstein, 1979). Thethree-dimensional finite element model used inthe present study provides the freedom to simu-late orthodontic force systems applied clinicallyand allows analysis of the response of thecraniofacial skeleton to the orthodontic loads inthree-dimensional space. The point of applica-tion, magnitude, and direction of a force mayeasily be varied to simulate the clinical situation.Thus, FEM would be an effective approach inthe investigation of the biomechanical behaviourof the craniofacial skeleton in three dimensions.

Analytical results of the FEM are highlydependent on the models developed, so theyhave to be constructed to be equivalent to realobjects in various aspects. The finite elementcomputations provide results which include errorsas a consequence of the geometry idealization,material characteristic properties, and boundaryconditions. Furthermore, the results are validonly for a single specific 12-year-old male. Froma structural engineering analyst's point of view,geometry idealization, material data selection, andassignment of boundary conditions of the presentanalysis are sound as long as the mechanical con-sequences of RME are investigated. In otherwords, the results are qualitatively valid even if,for instance, the Young's modulus or the geom-etry of the skull are an assumption. However, itwould be a pitfall to believe that the suppliednumerical values are applicable quantitativelyeven for this specific case study. The situationgets even worse if a generalization of the resultsis attempted for other patients. In this context, itis worth mentioning that comparative computa-tions with the present cranium have been con-ducted using the material and loading data ofTanne et al. (1987) and, respectively, of von Ehleret al. (1975), who used different skull geometriesthan the present 12-year-old male. Furthermore,the finite element models used in these threestudies are qualitatively and quantitatively distinct.

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BIOMECHANICAL EFFECTS OF RME 353

Force Direction in Degrees

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Figure 6 Comparison between computations by Tanneet al. (1987) and present study. In both computations thesame material and loading data are used, whereas the geo-metry of the cranium is distinct. The direction of the forcewas backward with a magnitude of 10 N, and applied to themaxillary first molar parallel to the functional occlusal plane.(a) Maximum principal stresses for the level of superiorridge of nasal fossa. (b) Horizontal displacements at theapex of the first molar as a function of the force direction.

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is found to separate supero-inferiorly in a non-parallel manner, the separation being pyramidalin shape with the base of the pyramid located atthe oral side of the bone, and the centre of rota-tion located near the fronto-maxillary suture(Krebs, 1959, 1964; Haas, 1961, 1970; Wertz,1968,1970;Mernikoglu et al., 1994, 1997).By usingimplants, Hicks (1978) reported that maxillae werefound to tip between -1 to +8 degrees relative toeach other. In a previous study, Mernikoglu et al.(1994) found that the basal maxillary anglechanged with a mean of 3 degrees with bondedRME. Thus, the findings of the previous studiesregarding the transversal rotation of the maxilla

Interestingly, the results obtained with the presentmodel supplied qualitatively similar results whencompared with both Tanne et ai. (1987) and vonEhler et al. (1975). For example, Figure 6a showsthe maximum principal stress distribution at thelevel of the superior ridge of the nasal fossa forcommon nodal points as obtained by the presentskull geometry with the loading and material dataand results of Tanne et al. (1987), and Figure 6bdepicts the horizontal displacements at the apexof the first molar as a function of varying forcedirections. Although there are quantitative differ-ences, qualitatively, the mechanical response ispredicted in the same manner, which is a posi-tive indication for the validity of the qualitativeconclusions.

Details of FEMs developed using CT scanninghave been previously published (Hart et al., 1992;Korioth et ai., 1992). Hart et al. (1992) used twodifferent methods to obtain the digitized descrip-tion of mandibular geometry, and suggested thatthe non-destructive method based on CT scansproved advantageous to a technique that involvedembedding the mandible in a plastic resin andcutting serial sections.

The subject in this study was a 12-year-oldmale, with a narrow maxillary base and bilateralposterior crossbite. He showed no craniofacialanomaly. According to the cephalometric anddental cast analyses, RME treatment was indi-cated. Different types of maxillary expansiondevices have been used by clinicians for rapidmaxillary expansion of the mid-palatal suture,and certain advantages of the bandless, indirectlyfabricated acrylic bonded RME appliances withocclusal coverage are reported (Howe, 1982;Spolyar, 1984; Alpern and Yorusko, 1987;Mernikoglu et al., 1994, 1997; Mernikoglu andIseri, 1997). The appliance model used in thepresent study simulates the same boundary con-ditions (predescribed displacements) as the acrylicbonded RME device.

The greatest widening was observed in thedento-alveolar structures, with the expansioneffect gradually decreasing through the upperstructures. Viewed anteriorly, the nasomaxillarycomplex rotated with the fulcrum of rotationaround the upper border of the orbita. Previousstudies have shown that the maxillary suture

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with RME are confirmed by the computationalresults of the present study.

Fried (1971) and Haas (1961, 1965) reportedthat the palatine processes of the maxilla werelowered as a result of the outward tilting of themaxillary halves. On the other hand, Davis andKronman (1969) noted that the palatal domeremained at its original height. The analyticalresults of the present study support the findingsof Fried (1971) and Haas (1961, 1965), and alsoindicate that the anterior region of the palatalprocesses lowered more than the posteriorregion. The maxillary central incisors and molarsshowed some extrusion, which was also demon-strated in previous studies (Byrum, 1971; Hicks,1978; Mernikoglu et al., 1994, 1997).

Many investigators have pointed out thatRME is not only limited to the palate but alsocauses dramatic changes in the craniofacial struc-tures. Kudlick (1973), in a study on a human dryskull that simulated the in vivo response of RMEsuggested that all craniofacial bones directlyarticulating with the maxilla were displaced exceptthe sphenoid bone. Gardner and Kronman (1971),in a study of RME in rhesus monkeys found thatthe lambdoid, parietal, and mid-sagittal suturesof the cranium showed evidence of disorientation,and in one animal these sutures split 1.5 mm.However, no displacement of parietal, frontal,and occipital bones was observed in the presentstudy.

Various investigators have shown that thereis an increase in the width of the nasal cavityfollowing expansion, particularly at the floorof the nose (Haas, 1961, 1965, 1970; Wertz,1970; Mernikoglu et al., 1994). As the maxillaeseparate, the outer walls of the nasal cavity movelaterally. The nasal cavity width gain averaged1.9 mm, but can widen as much as 8-10 mm atthe level of the inferior turbinates (Gray, 1975),while the more superior areas might move later-ally (Pavlin and Vukicevic, 1984). In 1968, Wertzconfirmed the advantage of rapid palatal expan-sion in improving nasal air flow in patientswith stenosis of the nasal airway, and reportedthe greatest benefit where the stenosis wasprimarily in the anterior-inferior region, whilethose patients with stenosis in the posterior-superior part of the nasal airway did not benefit

H. ISERI ET AL.

from palatal expansion. The numerical results ofthe present study demonstrate that the width ofthe nasal cavity at the floor of the nose increasedmarkedly compared with the superior parts, andthe posterior-superior region was moved slightlymedially (-0.3 mm) as previously speculated byPavlin and Vukicevik (1984).

Bishara and Staley (1987) suggest that themain resistance to mid-palatal suture openingis probably not in the suture itself, but in thesurrounding structures in the sphenoid andzygomatic bones. In fact, the highest stress levelsin this investigation were observed at thesphenoid and zygomatic bones, particularly atthe superior parts of the pterygoid plates ofthe sphenoid bone, and anterior part of thezygomatic bone (Table 1). In skull material, ithas been shown that the heavy interdigitation ofthe osseous surfaces between the palatine boneand the maxilla, and the pterygoid processesof sphenoid bone makes disarticulation difficultin the late juvenile and early adolescentperiods (Melsen and Melsen, 1982). Wertz (1970)mentioned that the confining effect of thepterygoid plates of the sphenoid bone minimizesdramatically the ability of the palatine bones toseparate at the mid-sagittal plane. Timms (1980)suggests that the pterygoid plates can bend onlyto a limited extent as pressure is applied to them,and their resistance to bending increases in theparts closer to the cranial base. On the other hand,the analytical results obtained in the presentstudy show that the inferior and middle parts ofthe pterygoid plates markedly displace or bendlaterally, and high stresses develop particularly inthe region close to the cranial base where theplates are more rigid. The deep anatomical effectof these orthopaedic appliances was also observedby the high stress levels in the areas of thezygomatic and maxillary bone, in the maxillarymolar area, zygomatic process and external wallof the orbita. Therefore, phenomena, such asdizziness and a feeling of heavy pressure on thebridge of the nose, under the eyes and generallythroughout the face, reported during RME(Zimring and Isaacson, 1965), could be due tothe forces in the nasal, sphenoid and zygomaticareas which are produced by activation of theRME appliances.

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Conclusions

The above findings indicate that RME not onlyproduces an expansion force at the intermaxillarysuture, but also high forces on various structuresin the craniofacial complex. Rapid displacementor deformation of the facial bones results in amarked amount of relapse in the long term,while relatively slower expansion of the maxillawould probably produce less tissue resistancein the nasamaxillary structures. Therefore, slowmaxillary expansion followed by RME, immedi-ately after the separation of the mid-palatalsuture, would stimulate the adaptation processesin the nasomaxillary structures, and also wouldresult in reduction of relapse in the post-retention period.

Future studies will aim to model the suture asa viscoelastic material with hardening properties,and experimental studies will be necessary todetermine the material properties of the suturalstructures under growing conditions.

Address for correspondence

Haluk IseriAnkara Universitesi

Di~ Hekimligi FakiiltesiOrtodonti Anabilim DahBesevlerAnkara 06500Turkey

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